Solved Practice Problems - Calculus IV | MTH 254, Study notes of Advanced Calculus

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Math 254 - Practice Problems Mon, Nov 7 Justify your reasoning. Iterated Integrals in Polar Coordinates iG ft f sin(x)e” dyda = (i sin(z) de) (i ev dy) 2. TYF)If the temperature on a plate is given by T(x, y) = 30027 + zy Kelvins (x, y in metérs), then at the point (1,0) in the direction (1,1) the temperature is changing at a rate of 601 Kelvins/meter. 3. 1{ Pon any function f(x,y), Z [ fiz,y) dy =0. zr fo 4. By changing to polar coordinates, find the volume under the surface f(z, y) = xy over the intersection of the regions 1 < 2% —y’ <4 and 0 fea rom «peo & smb ate” nae FF ttayd>( gest vr dvd | “4 S.keeeees “3 J Pde X) smoede) 02 £%